Coordinate Geometry

Find the distance between the following pairs of points:

Find the distance between the points (0, 0) and (36, 15). Can you now find the distance between the two towns A and B discussed in Section 7.2.

Determine if the points (1, 5), (2, 3) and (-2, -11) are collinear.

Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.

Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:

Find the point on the x-axis which is equidistant from (2, -5) and (-2, 9).

Find the values of y for which the distance between the points P(2, -3) and Q(10, y) is 10 units.

If Q(0, 1) is equidistant from P(5, -3) and R(x, 6), find the values of x. Also find the distances QR and PR.

Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (-3, 4).

Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.

Find the coordinates of the points of trisection of the line segment joining (4, -1) and (-2, -3).

Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).

Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis. Also find the coordinates of the point of division.

If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).

If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB.

Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order. [Hint: Area of a rhombus = 1/2 (product of its diagonals)]